Constrained Optimization for Retinal Curvature Estimation Using an Affine Camera

Abstract

We study retinal curvature estimation from multiple images that provides the fundamental geometry of human retina. We use an affine camera model due to its simplicity, linearity, and robustness. Moreover, the affine camera is suitable in this research because (1) NIH's retinal imaging protocols specify a narrow 30degC field-of-view in each eye and (2) each field has small depth variation. A major challenge is that there is a series of optics involved in the imaging process, including an actual fundus camera, a digital camera, and the human cornea, all of which cause significant non-linear distortions in the retinal images. In this work, we develop a new constrained optimization procedure that considers both the geometric shape of human retina and lens distortions. Moreover, the constrained optimization is implemented in the affine space because it is computationally efficient and robust to noise. Specifically, we amend the affine bundle adjustment algorithm by including a quadratic surface fitting error and the lens distortion correction into the cost function for constrained optimization. The experiments on both synthetic data and real retinal images show the effectiveness and robustness of the proposed algorithm.